Let $x$ and $y$ be two distinct prime numbers and $p = x^2y^2$, $q = xy^4$, $r = x^3y^2$. Find the HCF and LCM of $p$, $q$ and $r$. Further check if $ ext{HCF}(p, q, r) imes ext{LCM}(p, q, r) = p

Question

Let $x$ and $y$ be two distinct prime numbers and $p = x^2y^2$, $q = xy^4$, $r = x^3y^2$. Find the HCF and LCM of $p$, $q$ and $r$. Further check if $	ext{HCF}(p, q, r) 	imes 	ext{LCM}(p, q, r) = p 	imes q 	imes r$ or not.

Accepted Answer

Step 1: $	ext{HCF}(p, q, r) = xy^2$
Step 2: $	ext{LCM}(p, q, r) = x^3y^4$
Step 3: $	ext{HCF} 	imes 	ext{LCM} = x^4y^6$, but $p 	imes q 	imes r = x^6y^8$.
$	herefore 	ext{HCF} 	imes 	ext{LCM} 
eq p 	imes q 	imes r$.

Question

Solution